It is not easy to judge the validity of this assumption on the basis o f published figures It involves an evaluation o f effects o f nontariff barriers as well and it is not always possible to estimate

figures for the payments o f subsidies in different forms, hence the statement at best is a conjecture. However, as far as developing countries are concerned published figures show that tariff revenue has remained one o f the major source of government revenue. Motivated by this fact Feehan (1992) has derived efficiency rules for public input provision when the tariff is the sole source of revenue. For economies, whose government depends on tariff revenues, this assumption should be directly relevant.

Proof: Suppose not, and assume that Pi(f]i,f]_i) = PL*. Since P* is the lower bound of Pi we must have />((), tj^ ) >PL* for all 77_x e //_•. That is, Pt will not fall below P* whatever be the lobby expenditure of the other player(s). So,

n.(o,f)_.) >*,/?.(/>*)

> KtRt (P*) - fji

Hence T]i - 0 yields a higher payoff than r\i= f]i for r \= f]_i. This implies that fji is not a best response to fj_i, which further implies that (0,0) is not a Nash equilibrium of the game. A contradiction to the hypothesis. Q. E. D.

Thus the corollary shows that a Nash equilibrium of a Tariff Game will lead to a domestic price ratio that will always be different from the free trade price ratio. This completes the answer to the question of existence of an equilibrium in a productive economy that allows agents to behave strategically at least with respect to the issues related to the choice of tariff policies.

So far nothing has been said about the uniqueness of equilibrium of the game. The sufficient conditions for the uniqueness of equilibrium can be found in Friedman (1986). It suffices to note that the condition requires, together with other conditions, that the payoff function of each player be concave in their respective strategy set. Lemma 5.2 has shown it to be quasiconcave. Unless further restrictions are imposed on the rental function it cannot be guaranteed that the condition will be satisfied generally.

5.6 Conclusion

This chapter has extended the existence result obtained by Coggins, et al. for a productive economy that allows agents to behave strategically. It has shown that if the government is responsive to the lobby pressures of the interest groups, then there exists at least one non-trivial Nash equilibrium in a tariff game. Moreover, if the government is constrained to choose a tariff policy that is self-financing then all of the Nash

equilibria will imply a positive rationalized tariff rate. That is, the domestic price ratio in a Nash equilibrium will be different from the free trade price ratio.

In order to show the existence of an equilibrium in a lobbying exchange economy Coggins, et al. had to impose one restriction, which they called ‘own good bias’, on preferences. The proof outlined in this chapter did not require that assumption for a productive economy. This result occurred partly because in the Coggins, et al.'s model the endowment of good for each player was fixed but in our case sectoral output

levels, and hence the rental incomes are variable, and partly because Coggins, et al. measured player's payoffs in indirect utilities whereas this study used real net rental income as the payoffs to the players. It was thus possible to obtain much stronger results compared to previous studies with less severe assumptions. In fact, we obtained the existence results with the set of assumptions that were in Findlay and Wellisz (1982).

One of the limitations of the noncooperative Nash solution is that if there are multiple equilibria (see Magee, Brock and Young, 1989 for such cases) it cannot specify the mechanism through which one of the equilibria will be selected. It is also frequently the case that the Nash process may lead to a suboptimal solution of the game.13 To resolve this problem some mechanism of refining the Nash equilibria, such as subgame perfectness, are required.

One of the fundamental assumptions of the noncooperative game is that the players make decisions in isolation. If there is a distinct possibility of increasing their payoff through communication, negotiation and adoption of a joint maximizing strategy then the assumption that rational players in a competitive environment always play a noncooperative game does not seem plausible. In the tariff game, for example, each player may spend resources in competitive lobbying just to protect himself against the predatory lobbying of the other. It is possible that they both might have been receiving lower payoffs than they would receive if they had agreed not to compete against each other.

In the next chapter we change the rules of the game, and allow the players to discuss, negotiate, and make binding agreements that are payoff (welfare) improving. This takes us to the study of the game in a cooperative form. However, as Kreps (1990: 505) has remarked ‘this is not the cooperation borne of altruism or fondness of one’s fellow player. This is cooperation arising from a self-interested calculation of the benefits and losses that may accrue from “polite” behaviour’.

13 We noted in the review that Magee, Brock and Young (1989) have found several Prisoner's